Good evening, Doctor!
Of course, the clock belongs to you, and therefore, you may even crush it under your foot if you wish to. If that urge comes up, please contact us. Someone will almost certainly wish to take it off your hands.
Trouble is, as Dave said, once a clock is converted to say, a battery quartz movement, it is often irrevocably altered, and as such, its horological history is destroyed. We have no way of knowing what might happen. Someday, someone might be looking for just such a clock to learn something about its history or the history of similar clocks. Someone might desperately need a part to repair and bring back to life a similar clock. There's no way of telling what might happen.
If you could convert it to quartz without having to alter any of the existing parts, and if you could somehow save and keep all the old parts with the clock for future investigators, that would probably be fine. Some of us do just that, installing little bags or boxes inside old clocks to hold those extra parts.
Many of us hate those quartz movements where the second hand jumps from second to second and the movement makes an annoying "tic" at the same time. That's why, I believe, there are now quartz movements that silently move the second hand.
But can you convert it without altering the original? Can you keep the old parts with the old clock? If the old parts are stored in a drawer or a box somewhere, it is virtually a certainty that they'll eventually become permanently separated from the clock. Someday, someone will find them and wonder why you kept this old pile of "junk."
Someone else will see the clock on an auction site and think, "At last, I've found one of these! I want it!" only to be crushed to learn that it's been converted and the original parts are nowhere to be found.
Like you, most of us hate seeing old clocks sitting on a shelf, not working and gathering dust and rust. It would be nice for them to continue to do their duty and display the time for everyone to see.
It is often said that we do not own clocks. Instead, we merely have custody of them for future generations. Over time, there are fewer and fewer of them that survive. I hope yours won't become one of those.